An Egg Today and a Chicken Tomorrow: A Model of Social Security with Quasi-Hyperbolic Discounting

Strotz (1956) first suggested that individuals are more impatient when making short-run tradeoffs than long-run ones. Many experimental studies supports his conjecture. Motivated by recent evidence from the British Department of Work and Pension (2006), this paper applies this behavioral framework to retirement decisions. We propose a three-periods OLG model with quasi-hyperbolic consumers whosave for post retirement consumption in the first period and choose their retirement age in the second. We show that this behavioral assumption explains the observed drop in post retirement consumptiondue to lack of saving and the high level of voluntary (i.e. not due to disability or dismission from the firm) early exit from the labor force. When deciding about their retirement age, workers weight too much the costs of remaining at work (i.e. disutility of working, implicit tax on continued activity) and too little the benefits of postponed retirement (i.e. increase of the Bismarckian component of the pension formula), perceived as too far in the future. We investigate the implications of time inconsistent preferences for a political economy model in which voters determine simultaneously thesize and the degree of redistribution of the pension system. We show that, when voting over thepayroll tax, time inconsistent young workers, who look for a commitment device that increases boththeir saving and retirement age, form a coalition with rich in order to decrease the size of the system. When voting over the degree of redistribution, they form a coalition with poor individuals as to in-crease the at part of the pension formula. Our political model provides a political justification for the negative relationship between size and redistribution observed in most OECD countries (Disney 2004).